Stable pointsNote that stable points in modern terminology were referred to as properly stable points by Mumford [1]}. can be described as semistable points whose stabiliser groups are finite and whose orbits are closed in the semistable set. Often when the linearisation and group is fixed, we will drop the notation \(\mathcal {L}\)  and \(G\)  indicating the dependence of the semistable set on this linearisation and \(G\) . Variation of GIT describes the birational transformations between GIT quotients with respect to different \(G\) -linearisations [2]}, [3]}.
